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Basically I want to compute $x_{n+1} = (1/2)(x_n + 5/x_n)$.

On Mathematica, I wrote

h[1] := 2
h[n_] := h[n + 1] = (1/2)*(h[n] + 5/h[n])
h[2]

When I tried to compute h[2], I get this error message $RecursionLimit::reclim: "Recursion depth of 256 exceeded.

It works for easier sequences like f[n] = n f[n+1]. What is wrong?

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3  
That's because your second definition is wrong. Try h[n_] := h[n] = (1/2)*(h[n-1] + 5/h[n-1]). – J. M.♦ Oct 7 '12 at 2:27
It gave me the same message when I did h[3] – jak Oct 7 '12 at 2:40
2  
Did you Clear your previous definitions of h first? – rcollyer Oct 7 '12 at 2:43
h[1] := 2; h[n_] /; n >= 2 := h[n] = (1/2)(h[n - 1] + 5/h[n - 1]) implements the intended recursion. – whuber Oct 7 '12 at 19:42
RSolve[{h[n+1]==(1/2)*(h[n] + 5/h[n], h[1]==2}, h[n], n] gives what might be a plausible result. – Daniel Lichtblau Oct 7 '12 at 19:44

closed as too localized by rcollyer, rm -rf♦ Oct 7 '12 at 2:58

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